Gradient-Based Inverse Control for Noncanonical Nonlinear Systems with Unknown Input Backlash

Actuator backlash nonlinearity typically leads to delays, oscillations, and errors, thereby affecting the effective control of actuators in closed-loop systems. To suppress the effects of backlash, numerous adaptive backlash compensation schemes for nonlinear systems in canonical forms have been proposed. Due to the explicit relative degree of canonical systems, adaptive backlash inverse can be integrated with the backstepping frame-work, thus the adaptive backlash compensation problem for such systems can be quickly addressed. However, unlike the canonical system, the relative degree information of the noncanonical system is implicit, and its control gain is usually expressed as an uncertain control gain function. The combination of this function with the backlash nonlinearity makes handling backlash nonlinearity in noncanonical systems extremely challenging. To address this issue, this paper proposes an adaptive backlash inverse scheme to solve the backlash compensation problem with uncertain control gain functions. Additionally, by integrating this scheme with the gradient framework, an adaptive backlash inverse compensation control scheme is developed, ensuring that all signals in the noncanonical closed-loop system are bounded, and the system output asymptotically tracks the reference signal. Simulation results confirm the significant effectiveness and superiority of the proposed control scheme.